I had never played MW2 on the account that I have now. One day, me and some friends decided to hop on MW2 just for some nostalgia. I was a lvl 1 no prestige with nothing on my account. Later that day, I went back to MW3 and had a Prestige Token waiting for me. It couldn't have taken more than 2 hours for me to get it. I would guess it went through almost immediately.